No Cash: RoR formula?

[No Cash]

Let's say that I have a bankroll B, and that I bet 1 unit at a time on a wager with expectation E and variance V. What is my RoR before achieving a target K, where K>B? Has this been done? Is it in a book. An approximation formula is fine.

Also, how does the answer change if I bet, instead of 1 unit per round, some other amount f?

Thanks in advance. I know this is a hard question.

[Don Schlesinger]

> Let's say that I have a bankroll B, and that
> I bet 1 unit at a time on a wager with
> expectation E and variance V. What is my RoR
> before achieving a target K, where K>B?
> Has this been done? Is it in a book. An
> approximation formula is fine.

Norm and John have programmed this very complicated formula into their software, namely CV and BJRM.

Perhaps one of them will be able to post it here.

Better still, why not consult their software?

Don

[Norm Wattenberger]

as your name indicates, your RoR is zero. You have nothing to lose

Don?s trip ruin formula is on pages 161-164 in Blackjack Attack. But, that is single barrier. You appear to be looking for the double-barrier formula. That is, not just your chance of ruin ? but your chance of ruin before hitting a specified goal. This formula is a nightmare and, to my knowledge, Don has never published it. It took me two pages to write it down and is difficult to program because of wild swings in the contained series. However, I have a free online version that you can use at the below link. Click the link and then look for the Goal Probability Calculator.

QFIT Blackjack Calculators

[Don Schlesinger]

> Don?s trip ruin formula is on pages 161-164
> in Blackjack Attack . But, that is single
> barrier. You appear to be looking for the
> double-barrier formula. That is, not just
> your chance of ruin ? but your chance of
> ruin before hitting a specified goal. This
> formula is a nightmare and, to my knowledge,
> Don has never published it. It took me two
> pages to write it down and is difficult to
> program because of wild swings in the
> contained series. However, I have a free
> online version that you can use at the below
> link. Click the link and then look for the
> Goal Probability Calculator .

Note, too that the formula you refer to also has a time constraint: it needs to have a certain number of hands or hours stipulated. Of course, you could make that number ridiculously large if you wanted to.

Don